Question

Analyze the exploit formula of the arithmic sequence a n = 3.7 + 1/2 of in and report the 9th term round to the nearest tenth 10.6 4.28 8.2

Answer 1

To analyze the arithmetic sequence given by the formula \( a_n = 3.7 + \frac{1}{2} n \), we first need to determine the general term and then calculate the 9th term.

1. The general formula for the nth term of the arithmetic sequence is given by:
\[
a_n = a + (n-1)d
\]
Here, \( a \) is the first term, and \( d \) is the common difference.

2. From the formula \( a_n = 3.7 + \frac{1}{2} n \), we can identify:
- The first term, when \( n = 1 \):
\[
a_1 = 3.7 + \frac{1}{2} \cdot 1 = 3.7 + 0.5 = 4.2
\]
- The common difference \( d \) is \( \frac{1}{2} \).

3. To find the 9th term (\( a_9 \)):
\[
a_9 = 3.7 + \frac{1}{2} \cdot 9 = 3.7 + 4.5 = 8.2
\]

Thus, the 9th term, rounded to the nearest tenth, is **8.2**.

Among the options provided (10.6, 4.28, 8.2), the correct answer is **8.2**.